The Capacity Region of the Arbitrarily Varying MAC: With and Without Constraints

We determine both the random code capacity region and the deterministic code capacity region of the arbitrarily varying multiple access channel (AVMAC) under input and state constraints. For the AVMAC without constraints, the characterization due to Ahlswede and Cai is complete except for two cases, pointed out in the literature as an open problem. The missing piece is obtained as a special case of our results.

[1]  Hosseinigoki Fatemeh,et al.  The Gaussian interference channel in the presence of a malicious jammer , 2016 .

[2]  R. Ahlswede,et al.  Arbitrarily varying multiple-access channels. I. Ericson's symmetrizability is adequate, Gubner's conjecture is true , 1997, Proceedings of IEEE International Symposium on Information Theory.

[3]  Moritz Wiese,et al.  The Compound Multiple Access Channel With Partially Cooperating Encoders , 2011, IEEE Transactions on Information Theory.

[4]  Yossef Steinberg,et al.  The multiple-access channel with partial state information at the encoders , 2005, IEEE Transactions on Information Theory.

[5]  Johann-Heinrich Jahn,et al.  Coding of arbitrarily varying multiuser channels , 1981, IEEE Trans. Inf. Theory.

[6]  Brian L. Hughes,et al.  Nonconvexity of the capacity region of the multiple-access arbitrarily varying channel subject to constraints , 1995, IEEE Trans. Inf. Theory.

[7]  Ueli Maurer,et al.  Generalized privacy amplification , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[8]  A. El Gamal,et al.  Multiple user information theory , 1980, Proceedings of the IEEE.

[9]  Imre Csiszár,et al.  The capacity of the arbitrarily varying channel revisited: Positivity, constraints , 1988, IEEE Trans. Inf. Theory.

[10]  RUDOLF AHLSWEDE.  Arbitrarily varying channels with states sequence known to the sender , 1986, IEEE Trans. Inf. Theory.

[11]  S. Shafiee,et al.  Capacity of multiple access channels with correlated jamming , 2005, MILCOM 2005 - 2005 IEEE Military Communications Conference.

[12]  Thomas M. Cover,et al.  Network Information Theory , 2001 .

[13]  Oliver Kosut,et al.  The Gaussian interference channel in the presence of a malicious jammer , 2016, 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[14]  Yossef Steinberg,et al.  The Arbitrarily Varying Broadcast Channel With Causal Side Information at the Encoder , 2020, IEEE Transactions on Information Theory.

[15]  Suhas N. Diggavi,et al.  The worst additive noise under a covariance constraint , 2001, IEEE Trans. Inf. Theory.

[16]  D. Blackwell,et al.  The Capacity of a Class of Channels , 1959 .

[17]  R. Ahlswede.  Elimination of correlation in random codes for arbitrarily varying channels , 1978 .

[18]  Amos Lapidoth,et al.  The Multiple-Access Channel With Causal Side Information: Double State , 2013, IEEE Transactions on Information Theory.

[19]  Ning Cai,et al.  List Decoding for Arbitrarily Varying Multiple Access Channel Revisited: List Configuration and Symmetrizability , 2016, IEEE Transactions on Information Theory.

[20]  Prakash Narayan,et al.  Capacities of time-varying multiple-access channels with side information , 2002, IEEE Trans. Inf. Theory.

[21]  Yossef Steinberg,et al.  The Arbitrarily Varying Channel Under Constraints With Side Information at the Encoder , 2019, IEEE Transactions on Information Theory.

[22]  Amitalok J. Budkuley.  Jamming in fading Multiple Access Channels , 2015, 2015 Twenty First National Conference on Communications (NCC).

[23]  Roy D. Yates,et al.  The discrete memoryless compound multiple access channel with conferencing encoders , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[24]  Holger Boche,et al.  List decoding for arbitrarily varying multiple access channels with conferencing encoders , 2014, 2014 IEEE International Conference on Communications (ICC).

[25]  Imre Csiszár,et al.  Information Theory - Coding Theorems for Discrete Memoryless Systems, Second Edition , 2011 .

[26]  Bahareh Akhbari,et al.  Compound Multiple Access Channel with confidential messages , 2014, 2014 IEEE International Conference on Communications (ICC).

[27]  R. Ahlswede.  The Capacity Region of a Channel with Two Senders and Two Receivers , 1974 .

[28]  Gerhard Kramer,et al.  Topics in Multi-User Information Theory , 2008, Found. Trends Commun. Inf. Theory.

[29]  John A. Gubner.  On the deterministic-code capacity of the multiple-access arbitrarily varying channel , 1990, IEEE Trans. Inf. Theory.

[30]  Vinod M. Prabhakaran,et al.  Multiple Access Channels with Adversarial Users , 2019, 2019 IEEE International Symposium on Information Theory (ISIT).

[31]  Pierre A. Humblet,et al.  The capacity region of the totally asynchronous multiple-access channel , 1985, IEEE Trans. Inf. Theory.

[32]  John A. Gubner.  On the capacity region of the discrete additive multiple-access arbitrarily varying channel , 1992, IEEE Trans. Inf. Theory.

[33]  John A. Gubner.  Deterministic Codes for Arbitrarily Varying Multiple-Access Channels , 1988 .

[34]  John A. Gubner.  State constraints for the multiple-access arbitrarily varying channel , 1991, IEEE Trans. Inf. Theory.

[35]  Thomas H. E. Ericson,et al.  Exponential error bounds for random codes in the arbitrarily varying channel , 1985, IEEE Trans. Inf. Theory.

[36]  Shlomo Shamai,et al.  Cooperative Multiple-Access Encoding With States Available at One Transmitter , 2008, IEEE Trans. Inf. Theory.

[37]  D. Blackwell,et al.  The Capacities of Certain Channel Classes Under Random Coding , 1960 .

[38]  Te Sun Han,et al.  A new achievable rate region for the interference channel , 1981, IEEE Trans. Inf. Theory.

[39]  Imre Csiszár,et al.  Capacity of the Gaussian arbitrarily varying channel , 1991, IEEE Trans. Inf. Theory.

[40]  Sirin Nitinawarat.  On the Deterministic Code Capacity Region of an Arbitrarily Varying Multiple-Access Channel Under List Decoding , 2013, IEEE Trans. Inf. Theory.

[41]  Aylin Yener,et al.  MIMO Multiple Access Channel With an Arbitrarily Varying Eavesdropper: Secrecy Degrees of Freedom , 2013, IEEE Trans. Inf. Theory.

[42]  Aaron D. Wyner,et al.  Recent results in the Shannon theory , 1974, IEEE Trans. Inf. Theory.

[43]  Remi A. Chou,et al.  The Gaussian multiple access wiretap channel when the eavesdropper can arbitrarily jam , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[44]  János Körner,et al.  General broadcast channels with degraded message sets , 1977, IEEE Trans. Inf. Theory.

[45]  Vinod M. Prabhakaran,et al.  Byzantine Multiple Access , 2019, ArXiv.

[46]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[47]  Moritz Wiese,et al.  Multiple Access Channels with Cooperating Encoders , 2013 .

[48]  Moritz Wiese,et al.  The Arbitrarily Varying Multiple-Access Channel With Conferencing Encoders , 2011, IEEE Transactions on Information Theory.

[49]  Imre Csiszár,et al.  Arbitrarily varying channels with general alphabets and states , 1992, IEEE Trans. Inf. Theory.

[50]  D. Slepian,et al.  A coding theorem for multiple access channels with correlated sources , 1973 .

[51]  Matthieu R. Bloch,et al.  Keyless covert communication over Multiple-Access Channels , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[52]  Himanshu Asnani,et al.  On the Sum-capacity of Compound MAC Models with Distributed CSI and Unknown Fading Statistics , 2019, 2019 53rd Annual Conference on Information Sciences and Systems (CISS).